Season the fish with salt and pepper and turn in flour, shaking off excess.
-Heat 1 teaspoon butter and 1 teaspoon oil in a pan until the butter foam begins to subside. Lay in the fillets and saute for about a minute on each side, just until the fish begins to take on a light springiness to the touch. -Do not overcook; if the fish flakes, it is overdone.
-Remove to a hot platter and sprinkle minced fresh parsley over the fish. Rapidly wipe the pan clean with paper towels (so the flour residue will not speckle the butter to come – or use a fresh pan).
-Heat remaining butter in the pan, swishing it about and letting it brown lightly. Remove the pan from heat, squeeze in the juice of half a lemon, and capers before spooning the hot butter over the fish.